A new procedure for ground response curve (GRC) in strain-softening surrounding rock

The viewpoint that the ground initial elastic displacement and the interaction between the ground response curve (GRC) and support response curve (SRC) in the surrounding rock should be considered at the same time in the mechanical analysis of the circular tunnel is proposed, and its solution method is also established. Meanwhile, in order to consider the effect of the intermediate principle stress, Drucker-Prager criterion is introduced to describe the yield property of the surrounding rock. The calculation example indicates that the final radial displacement of the tunnel circumference will increase when the ground initial elastic displacement in the surrounding rock is considered before the support structure is applied, which indicates that it is necessary to consider the ground initial elastic displacement in the surrounding rock before the support structure is applied. With increasing the support resistance force and the initial field stress, the plastic zone radius in the surrounding rock and the radial displacement of the tunnel circumference will decrease and increase, respectively, while with increasing the rock internal friction angle and cohesion, the plastic zone radius in the surrounding rock and the radial displacement of the tunnel circumference both decrease. Meanwhile, with the stress Lode parameter increasing from −1 to 1, the plastic zone radius in the surrounding rock and the radial displacement of the tunnel circumference both greatly decrease and then slightly increase. It indicates that the intermediate principle stress has some effect on the calculation results.

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The ground response curve of underwater tunnels, excavated in a strain-softening rock mass

Geomechanics and Engineering ◽

10.12989/gae.2015.8.3.323 ◽

2015 ◽

Vol 8 (3) ◽

pp. 323-359 ◽

Cited By ~ 6

Author(s):

Ahmad Fahimifar ◽

Hamed Ghadami ◽

Masoud Ahmadvand

Keyword(s):

Rock Mass ◽

Response Curve ◽

Strain Softening ◽

Ground Response

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Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0253 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Sheng Yu-ming ◽

Li Chao ◽

Xia Ming-yao ◽

Zou Jin-feng

Keyword(s):

Finite Element ◽

Principal Stress ◽

Stress Condition ◽

Strain Softening ◽

Numerical Solutions ◽

Three Dimensional ◽

Strength Criterion ◽

Surrounding Rock ◽

Flow Rule ◽

Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

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Back Analysis for Mass Parameters of Tunnel Surrounding Rock

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.170-173.20 ◽

2012 ◽

Vol 170-173 ◽

pp. 20-24 ◽

Cited By ~ 1

Author(s):

Kai Cui ◽

Xue Kai Pan

Keyword(s):

Deformation Mechanism ◽

Strain Softening ◽

Back Analysis ◽

Surrounding Rock ◽

Tunnel Engineering ◽

Railway Tunnel ◽

Displacement Back Analysis ◽

Information Construction ◽

Engineering Information ◽

The Common

Tunnel engineering information construction has been widely used, and the back analysis is its core. As the common useful method, displacement back analysis is of special advantages. This paper introduces the calculative method based on the application in a railway tunnel. The result shows that strain softening model can be used to simulate the large deformation mechanism of surrounding rock.

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A Numerical Approach for the Quasi-Plane Strain-Softening Problem of Cylindrical Cavity Expansion Based on the Hoek-Brown Failure Criterion

Mathematical Problems in Engineering ◽

10.1155/2016/3698525 ◽

2016 ◽

Vol 2016 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Jin-feng Zou ◽

Jia-min Du

Keyword(s):

Plastic Strain ◽

Plane Strain ◽

Principal Stress ◽

Failure Criterion ◽

Strain Softening ◽

Axial Direction ◽

Intermediate Principal Stress ◽

Surrounding Rock ◽

Cavity Expansion ◽

Cylindrical Cavity Expansion

This paper focuses on a novel approach for the quasi-plane strain-softening problem of the cylindrical cavity expansion based on generalized Hoek-Brown failure criterion. Because the intermediate principal stress is deformation-dependent, the quasi-plane strain problem is defined to implement the numerical solution of the intermediate principal stress. This approach assumes that the initial total strain in axial direction is a nonzero constant (ε0) and the plastic strain in axial direction is not zero. Based on 3D failure criterion, the numerical solution of plastic strain is given. Solution of the intermediate principal stress can be derived by Hooke’s law. The radial and circumferential stress and strain considering the intermediate principal stress are obtained by the proposed approach of the intermediate principal stress, stress equilibrium equation, and generalized H-B failure criterion. The numerical results can be used for the solution of strain-softening surrounding rock. In additional, the validity and accuracy of the proposed approach are verified with the published results. At last, parametric studies are carried out using MATLAB programming to highlight the influences of the out-of-plane stress on the stress and displacement of surrounding rock.

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A New Unified Solution for Circular Tunnels Based on Generalized SMP Criterion considering the Strain Softening and Dilatancy

Advances in Civil Engineering ◽

10.1155/2019/1684707 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10

Author(s):

Qifeng Guo ◽

Jiliang Pan ◽

Xinghui Wu ◽

Xun Xi ◽

Meifeng Cai

Keyword(s):

Internal Friction ◽

Plastic Zone ◽

Strain Softening ◽

Friction Angle ◽

Surrounding Rock ◽

Internal Friction Angle ◽

Plastic State ◽

Circular Tunnel ◽

Dilatancy Angle ◽

Elastic Plastic

According to the strain-softening characteristics of rock mass, an ideal elastic strain-softening model is developed, and the surrounding rock of tunnels is subdivided into the plastic broken zone, plastic strain-softening zone, and elastic zone. Based on the generalized spatially mobilized plane criterion, an elastic-plastic analytical solution of a circular tunnel is derived. The effects of intermediate principal stress, strain softening, and dilatancy are considered in the unified solution. The stress, displacement, and plastic zone radius of surrounding rock based on the SMP criterion are compared with those based on the Mohr–Coulomb criterion. Furthermore, the effects of parameters such as the softening modulus, dilatancy angle, and internal friction angle on the deformation and stress of tunnels are discussed. It has been found that the larger the dilatancy angle is, the larger the plastic zone displacement and the radius of the broken zone are. The larger the internal friction angle, the smaller the sizes of the plastic zone, the strain-softening zone, and the broken zone are. The deformation of surrounding rock in the broken zone is more sensitive to the internal friction angle than that in the strain-softening zone. The unified solution based on the SMP criterion provides a well understanding for the elastic-plastic state of tunnels, which can be the guidance for tunnel excavations and support designs.

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An Improved Stress and Strain Increment Approaches for Circular Tunnel in Strain-Softening Surrounding Rock Considering Seepage Force

Advances in Materials Science and Engineering ◽

10.1155/2019/2075240 ◽

2019 ◽

Vol 2019 ◽

pp. 1-17 ◽

Cited By ~ 1

Author(s):

Ling Wang ◽

Jin-feng Zou ◽

Yu-ming Sheng

Keyword(s):

Rock Mass ◽

Plastic Zone ◽

Radial Displacement ◽

Axisymmetric Problem ◽

Strain Softening ◽

Strain Increment ◽

Surrounding Rock ◽

Stress And Strain ◽

Seepage Force ◽

Circular Tunnel

Considering the effect of seepage force, a dimensionless approach was introduced to improve the stress and strain increment approach on the stresses and radial displacement around a circular tunnel excavated in a strain-softening generalized Hoek–Brown or Mohr–Coulomb rock mass. The circular tunnel can be simplified as axisymmetric problem, and the plastic zone was divided into a finite number of concentric rings which satisfy the equilibrium and compatibility equations. Increments of stresses and strains for each ring were obtained by solving the equilibrium and compatibility equations. Then, the stresses and displacements in softening zone can be calculated. The correctness and reliability of the proposed approach were performed by the existing solutions.

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